Since Mathematica 9, neither the front end nor the kernel launch Java automatically anymore, as our Java specialists have confirmed to me.
So if the reinstallation of Java on your machine fixed your previous inability to start Mathematica, is it possible that you are loading any specific packages or such at start-up, through according code in the init.m file?
Also, could you please describe what your original situation was:
- Was your Mavericks update a complete reinstall on your system?
- Did you install Java before trying to run Mathematica the first time?
- Did you try a preferences reset or a clean reinstall of Mathematica as described in the articles below help:
http://support.wolfram.com/kb/4730 + a subsequent installation
It would help determining whether all of you have actually encountered the same or different situations.